The generator matrix

 1  0  0  0  0  1  1  1  0  X  0  0  X  1  1  1  1  1  1  1  X  1  0  1  X  X  0  0  X  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  X  X  1  X  1 2X  1  1  1  1  X  1  1  1 2X  1  X  1  1  1  1  X 2X  1  1  1  0  1  1  1  1  X  1 2X  1  1  X  1  1  1  1  1  1  1  1  1
 0  1  0  0  0  0  0  0 2X  X  1  1  1  2  2  2 2X+2 2X 2X+2 X+2  1 X+2  1  2  1  1  1  0  0  1 X+1 X+1  X  X X+1 X+1  2  X 2X  2  1 2X+1  1  X  1  0 2X+1  0 2X+2  1  0 X+2 X+1 2X+1  1  0 2X+1 2X+2  1  1  1 2X+2  2 2X+2  1  1  1 2X+1 2X X+1  1  X X+1  X X+1  1  X  1 2X+1  0  1 2X X+1  2  1 2X+1 2X+2  0  0  0
 0  0  1  0  0  0  1 2X+1  1  1  1  X 2X+2  0 2X+2 2X+1  2  2 2X+1 2X+2  1 X+1  1 2X  0  X 2X+1  X  1 X+1 2X+2 2X+2  2 2X+1 2X  X 2X X+2  1 X+2 2X+1  0  X  1  2 2X  1  1 2X 2X  0 2X+2 2X 2X+2  1 2X X+1 2X+2 X+2 X+1  0 2X+1 X+2 2X+2  1  1  2 2X+1 X+1 X+2  1  1  1 X+2 2X+2 2X  X X+2 2X  2  X 2X  X 2X+1  X 2X+2  0 2X+1 X+1  X
 0  0  0  1  0  1  1 2X+2 2X+1  1 X+1 X+2  1 X+2 2X  2 2X+1 2X+2  1  X 2X+2 X+1 X+2  0  0  1  X  1 2X+2  0 2X+2  0  2  1  2 2X+1 2X X+1 2X+2 2X+2  2 X+1 2X+2 2X 2X+2  1  X X+1 2X+2  X X+1 2X  2  X X+1  0  2 X+1 2X 2X+2 X+2  1  0 2X+1  X 2X+1 2X+1 2X+1  2 2X+2 X+1  1 2X+1  0 X+2 X+2 2X+2 2X+2  1  1 X+1 2X+2 2X X+1 2X+1 2X  0 2X+1  2  X
 0  0  0  0  1  2  X 2X+2 X+2  1  X  1 2X+1 2X+2  X  0 2X+2  0  1 2X+1  X  2 2X+2 2X+1  1  2  2  1  X  1  0 X+2 X+1 2X+1 X+1 2X 2X+2  0  2 X+1  X  1  2 2X+2  1 X+2 2X  0 2X+1  2 2X+1 X+2  X 2X+1 X+1  0  2 2X  0 X+2 X+2  X X+1  0 X+2 2X  0 2X+2 2X 2X+2 X+2  2 2X+2  1 2X 2X  0 X+2 X+1 2X+2  0 2X+2 X+2  X  X 2X+1  2 X+1 2X  X
 0  0  0  0  0 2X  0 2X 2X  X  0  X  X 2X  0  0 2X  0  X  X  0 2X 2X  X  X 2X 2X 2X 2X 2X 2X  0 2X 2X 2X 2X  0 2X  X  0  X  0  0  X 2X  0 2X  X  0  X  0  X  X 2X 2X 2X  0 2X  X  X 2X  0 2X  X  0  X  X 2X  X  X  X  0  X 2X  X 2X  0  0  X  X  X  X 2X  X  X  X  0  X  0 2X

generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+140x^159+108x^160+768x^161+728x^162+744x^163+1812x^164+1818x^165+1452x^166+3600x^167+3148x^168+2184x^169+5670x^170+4600x^171+3522x^172+7590x^173+6076x^174+4626x^175+9366x^176+8072x^177+5388x^178+11364x^179+8904x^180+6186x^181+11694x^182+8408x^183+5622x^184+10482x^185+7142x^186+4344x^187+7878x^188+4892x^189+2778x^190+4710x^191+3004x^192+1650x^193+2520x^194+1328x^195+558x^196+918x^197+554x^198+162x^199+276x^200+182x^201+42x^202+60x^203+34x^204+24x^206+4x^210+6x^213+4x^216+2x^219+2x^240

The gray image is a linear code over GF(3) with n=270, k=11 and d=159.
This code was found by Heurico 1.16 in 776 seconds.